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Feynman diagram techniques in condensed matter physics

Author: Radi A Jishi
Publisher: Cambridge : Cambridge University Press, 2013.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"A concise introduction to Feynman diagram techniques, this book shows how they can be applied to the analysis of complex many-particle systems, and offers a review of the essential elements of quantum mechanics, solid state physics and statistical mechanics. Alongside a detailed account of the method of second quantization, the book covers topics such as Green's and correlation functions, diagrammatic techniques,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Jishi, Radi A., 1955-
Feynman diagram techniques in condensed matter physics.
Cambridge : Cambridge University Press, 2013
(DLC) 2013005735
(OCoLC)826076046
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Radi A Jishi
ISBN: 9781107341753 1107341752 113917777X 9781139177771 9781299707757 1299707750 9781107345508 1107345502 9781107357624 1107357624 9781107348004 1107348005
OCLC Number: 846495113
Description: 1 online resource
Contents: Preface --
1 A brief review of quantum mechanics --
1.1 The postulates --
(I) The quantum state --
(II) Observables --
(III) Time evolution --
(IV) Measurements --
(V) Wave function of a system of identical particles --
1.2 The harmonic oscillator --
Further reading --
Problems --
2 Single-particle states --
2.1 Introduction --
2.2 Electron gas --
2.3 Bloch states --
2.4 Example: one-dimensional lattice --
2.5 Wannier states --
2.6 Two-dimensional electron gas in a magnetic field --
Further reading --
Problems --
3 Second quantization --
3.1 N-particle wave function --
3.2 Properly symmetrized products as a basis set --
3.3 Three examples --
3.4 Creation and annihilation operators --
3.5 One-body operators --
3.6 Examples --
3.7 Two-body operators --
3.8 Translationally invariant system --
3.9 Example: Coulomb interaction --
3.10 Electrons in a periodic potential --
3.11 Field operators --
Further reading --
Problems --
4 The electron gas --
4.1 The Hamiltonian in the jellium model --
4.2 High density limit --
4.3 Ground state energy --
Further reading --
Problems --
5 A brief review of statistical mechanics --
5.1 The fundamental postulate of statistical mechanics --
5.2 Contact between statistics and thermodynamics --
5.3 Ensembles --
5.4 The statistical operator for a general ensemble --
5.5 Quantum distribution functions --
Further reading --
Problems --
6 Real-time Green's and correlation functions --
6.1 A plethora of functions --
6.2 Physical meaning of Green's functions --
6.3 Spin-independent Hamiltonian, translational invariance --
6.4 Spectral representation --
6.5 Example: Green's function of a noninteracting system --
6.6 Linear response theory --
6.7 Noninteracting electron gas in an external potential --
6.8 Dielectric function of a noninteracting electron gas. 6.9 Paramagnetic susceptibility of a noninteracting electron gas --
6.10 Equation of motion --
6.11 Example: noninteracting electron gas --
6.12 Example: an atom adsorbed on graphene --
Further reading --
Problems --
7 Applications of real-time Green's functions --
7.1 Single-level quantum dot --
7.2 Quantum dot in contact with a metal: Anderson's model --
7.3 Tunneling in solids --
Further reading --
Problems --
8 Imaginary-time Green's and correlation functions --
8.1 Imaginary-time correlation function --
8.2 Imaginary-time Green's function --
8.3 Significance of the imaginary-time Green's function --
8.4 Spectral representation, relation to real-time functions --
8.5 Example: Green's function for noninteracting particles --
8.6 Example: Green's function for 2-DEG in a magnetic field --
8.7 Green's function and the U-operator --
8.8 Wick's theorem --
8.9 Case study: first-order interaction --
8.10 Cancellation of disconnected diagrams --
Further reading --
Problems --
9 Diagrammatic techniques --
9.1 Case study: second-order perturbation in a system of fermions --
9.2 Feynman rules in momentum-frequency space --
9.3 An example of how to apply Feynman rules --
9.4 Feynman rules in coordinate space --
9.5 Self energy and Dyson's equation --
9.6 Energy shift and the lifetime of excitations --
9.7 Time-ordered diagrams: a case study --
9.8 Time-ordered diagrams: Dzyaloshinski's rules --
Further reading --
Problems --
10 Electron gas: a diagrammatic approach --
10.1 Model Hamiltonian --
10.2 The need to go beyond first-order perturbation theory --
10.3 Second-order perturbation theory: still inadequate --
10.4 Classification of diagrams according to the degree of divergence --
10.5 Self energy in the random phase approximation (RPA) --
10.6 Summation of the ring diagrams --
10.7 Screened Coulomb interaction. 10.8 Collective electronic density fluctuations --
10.9 How do electrons interact? --
10.10 Dielectric function --
10.11 Plasmons and Landau damping --
10.12 Case study: dielectric function of graphene --
Further reading --
Problems --
11 Phonons, photons, and electrons --
11.1 Lattice vibrations in one dimension --
11.2 One-dimensional diatomic lattice --
11.3 Phonons in three-dimensional crystals --
11.4 Phonon statistics --
11.5 Electron-phonon interaction: rigid-ion approximation --
11.6 Electron-LO phonon interaction in polar crystals --
11.7 Phonon Green's function --
11.8 Free-phonon Green's function --
11.9 Feynman rules for the electron-phonon interaction --
11.10 Electron self energy --
11.11 The electromagnetic field --
11.12 Electron-photon interaction --
11.13 Light scattering by crystals --
11.14 Raman scattering in insulators --
Further reading --
Problems --
12 Superconductivity --
12.1 Properties of superconductors --
12.2 The London equation --
12.3 Effective electron-electron interaction --
12.4 Cooper pairs --
12.5 BCS theory of superconductivity --
12.6 Mean field approach --
12.7 Green's function approach to superconductivity --
12.8 Determination of the transition temperature --
12.9 The Nambu formalism --
12.10 Response to a weak magnetic field --
12.11 Infinite conductivity --
Further reading --
Problems --
13 Nonequilibrium Green's function --
13.1 Introduction --
13.2 Schrodinger, Heisenberg, and interaction pictures --
13.3 The malady and the remedy --
13.4 Contour-ordered Green's function --
13.5 Kadanoff-Baym and Keldysh contours --
13.6 Dyson's equation --
13.7 Langreth rules --
13.8 Keldysh equations --
13.9 Steady-state transport --
13.10 Noninteracting quantum dot --
13.11 Coulomb blockade in the Anderson model --
Further reading --
Problems --
Appendix A: Second quantized form of operators --
A.1 Fermions. A.2 Bosons --
Appendix B: Completing the proof of Dzyaloshinski's rules --
Appendix C: Lattice vibrations in three dimensions --
C.1 Harmonic approximation --
C.2 Classical theory of lattice vibrations --
C.3 Vibrational energy --
C.4 Quantum theory of lattice vibrations --
Appendix D: Electron-phonon interaction in polar crystals --
D.1 Polarization --
D.2 Electron-LO phonon interaction --
References --
Index.
Responsibility: Radi A. Jishi, California State University.
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Abstract:

This introduction to Feynman diagram techniques shows their application to the analysis of complex many-particle systems. Detailed derivations of formulas, case studies and chapter exercises with  Read more...

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